A308819 Product of prime powers <= n.

1, 1, 2, 6, 24, 120, 120, 840, 6720, 60480, 60480, 665280, 665280, 8648640, 8648640, 8648640, 138378240, 2352430080, 2352430080, 44696171520, 44696171520, 44696171520, 44696171520, 1028011944960, 1028011944960, 25700298624000, 25700298624000, 693908062848000

Offset: 0

Author

Ilya Gutkovskiy, Jun 26 2019

Keywords

• nonn

Comments

a(n) is the smallest number that's divisible by all numbers less than or equal to n. - Keith F. Lynch, Apr 24 2025

Examples

			a(9) = 60480 because 2, 3, 4, 5, 7, 8, 9 are the prime powers less than or equal to 9 and 2 * 3 * 4 * 5 * 7 * 8 * 9 = 60480.
		

Crossrefs

Cf. A000961, A024923, A034386, A065515, A074793, A100994, A179215, A246655.

Programs

Mathematica

a[n_] := Product[If[PrimePowerQ[k], k, 1], {k, 1, n}]; Table[a[n], {n, 0, 27}]
Module[{nn=50,ppwr},ppwr=Select[Range[nn],PrimePowerQ[#]&];Table[Times@@ Select[ ppwr,#<= n&],{n,0,nn}]] (* Harvey P. Dale, Apr 03 2024 *)

PARI

a(n) = prod(k=1, n, if (isprime(k) || isprimepower(k), k, 1)); \\ Michel Marcus, Jun 27 2019